Professor Fendley´s main field of research is on non-perturbative approaches to field theory and statistical mechanics. These methods are valuable for exploring the large number of interesting systems with strong couplings in particle physics and condensed-matter physics. Theoretical physicists have used field theory to successfully describe the strong and electroweak interactions of particle physics, and all sorts of condensed-matter physics. Most of our understanding has been based on perturbative calculations, valid when some coupling constant is small. Nevertheless, we believe that quantum field theories describe subatomic physics even when couplings are large; for example, quantum chromodynamics should still describe the physics of confinement, which by its nature requires strong couplings. Moreover, experimental advances have allowed extensive scrutiny of condensed-matter systems like the quantum Hall effect, quantum impurities and spin chains where the interactions are strong. Many of these systems exhibit fully non-Fermi-liquid behavior, meaning that one usually cannot even formulate a perturbation theory around free electrons. Prof. Fendley works on the Bethe Ansatz, supersymmetry, conformal field theory, and other methods of finding exact results in these strongly-interacting systems. These methods are applicable to experimentally-realizable systems as well as to interesting theories arising in mathematical physics.